In a right triangle, he measure of one acute angle is 3 times the sum of the other acute angle and 8, Find the measure of angle 1 and 2
The measure of angles 1 and 2 are 16.5 and 73.5 respectively.
The sum of the two acute angles is complementary.
Let the complementary acute angles be x and y
Since they form a right angle triangle, hence;
x + y = 90 ............................. 1
If the measure of one acute angle is 3 times the sum of the other acute angle and 8, this is expressed as x = 3(y + 8)
Substitute the value of x into the equation 1 as shown:
3(y+8) + y = 90
3y + 24 + y = 90
4y + 24 = 90
4y = 90 - 24
4y = 66
y = 66/4
y = 16.5
Get the other acute angle:
x = 90 - y
x = 90 - 16.5
x = 73.5 degrees
Hence the measure of angles 1 and 2 are 16.5 and 73.5 respectively.
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____ as 9 hundreds is 9 thousands
Ten as 9 hundreds is 9 thousands.
What is place value?
Place value is the value of each digit in a number.
For example 5 in 350 is 5 tens or 50.
The given digit is 9 thousand which can be written as 9,000
It can be written as,
9,000 = 9 x 1000
or,9,000 = 9 x 10 x 100
So, for require 9 hundreds multiplying 9 by 100 in the above expression
9,000 = 10 x 900
which can be described as Ten as 9 hundreds is 9 thousand.
Hence, ten as 9 hundreds is 9 thousands
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10 as 9 hundreds is 9 thousands.
How to Obtain place values from a given number ?Suppose a number 12345 is given this can be written as
10000 + 2000 + 300 + 40 + 5 if we sum up all these we will get back our given number.
Now if we are asked what is the place value of 2 & 4
So, the place value of 2 in the given number is 2000 & the place value of 4 is 40.
Place value is defined as the value based on the position of that number whether it's in thousand's place or ten's or in 1's place.
In the given question
___ as 9 hundreds is 9 thousand
⇒ ____ as 900 is 9000
if we divide 9000/900 = 10 we will get our answer.
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If the CPI (consumer price index) of 141 increased 8.3 % this year. What was the end of year CPI?
If the CPI increased by 8.3%, therefore this means that there was a fractional increase of 0.083. So amount increased is:
CPI increase = 141 * 0.083 = 11.703
Therefore the end of year CPI is the sum of the original and the increase:
end of year CPI = 141 + 11.703 = 152.703
Answer:
152.703
Fifty eight thousand kilograms of solid waste is equivalent to how many metric tons
Answer:58 metric ton
Step-by-step explanation:
Given
Fifty eight thousand kilogram of solid waste
We need to convert it into metric tons
and we know 1 metric ton is equivalent to one thousand kilogram i.e. 1000 kg
so 58,000 kg is equivalent to 58 metric ton
in six years, clem kadiddlehopper will be 5 times as old as he was 26 years ago how old is he now?
The question involves setting up an equation to determine Clem Kadiddlehopper's current age based on his age in six years and 26 years ago. By solving the equation x + 6 = 5(x - 26), we find that Clem is currently 34 years old.
Explanation:Explanation:
The question asks us to determine Clem Kadiddlehopper's current age based on information about his age in future and past years. Let's define Clem's current age as x years old.
In six years, he will be x + 6 years old. It is stated that in six years, Clem will be five times as old as he was 26 years ago. Since 26 years ago he was x - 26 years old, we can write the equation: x + 6 = 5(x - 26).
To find Clem's age, we will solve the equation:
x + 6 = 5(x - 26)x + 6 = 5x - 1304x = 136x = 34Therefore, Clem Kadiddlehopper is currently 34 years old.
A bag contains 20 red tickets and 12 blue tickets. What is the probability of randomly selecting a blue ticket from the bag? A. 4/5 B. 3/11 C. 3/8 D. 1/2
what is 50 divided by 2.5 divided by 0.04
The value of the 50 divided by 2.5 divided by 0.04 is equal to 500.
To calculate 50 divided by 2.5 divided by 0.04, should follow the order of operations,
which is parentheses, exponents, multiplication and division (from left to right), and finally addition and subtraction (from left to right).
However, there are no parentheses or exponents in this expression, so we can proceed directly to multiplication and division:
50 ÷ 2.5 ÷ 0.04
First, divide 50 by 2.5:
50 ÷ 2.5 = 20
Next, divide the result (20) by 0.04:
20 ÷ 0.04 = 500
Therefore, 50 divided by 2.5 divided by 0.04 equals 500.
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Which of the following sets shows all the numbers from the set {2, 3, 4, 5} that are part of the solution to the inequality 4n + 6 > 22?
Find the solution of the given initial value problem y'+2/ty=cost/t^2
The ray GJ is the angle bisector of angle FGH and Measurement FGH =50 degrease what is the measurement of angle FGJ
Which unit would you use to measure the amount of water in a swimming pool mL, kg, L or cm
Rick works off commission. He earns 10 percent of all manufacturing equipment he sells. If he made a sale of $9,000, how much was his commission?
commission would be 9000 * 0.10 = 900
he would make $900
The formula for glue says to add 50ML
of hardener to each container of resin. How much hardener should be added to 15 containers of resin?
Final answer:
To find out the total hardener needed for 15 containers of resin, multiply 15 by the amount per container, 50ML, which equals 750ML of hardener in total.
Explanation:
To calculate the total amount of hardener needed for 15 containers of resin, we use a simple multiplication. We have been given that each container requires 50ML of hardener. Therefore, we multiply the number of containers by the amount of hardener needed per container.
Calculation:
Number of containers × Amount of hardener per container = Total amount of hardener
15 containers × 50ML/container = 750ML
Thus, for 15 containers of resin, you would need to add a total of 750ML of hardener.
What is the solution of the proportion 5/x+4=3/x-2
Jay went to an amusement park. The park charges an entrance fee of $10.50 and $4.50 for every ride. Jay spent $46.50 on entrance fees and rides. Which fuction can be used to find the number of rides he went on?
The function to find the number of rides Jay went on is [tex]\( 10.50 + 4.50x = 46.50 \)[/tex]
Let x be the number of rides Jay went on.
The cost of the entrance fee is $10.50, and the cost per ride is $4.50. The total amount Jay spent is $46.50. The equation representing this scenario is:
[tex]\[10.50 + 4.50x = 46.50\][/tex]
To find the number of rides, you can solve for x:
1. Subtract the entrance fee from the total amount:
[tex]\[ 46.50 - 10.50 = 36.00 \][/tex]
2. Divide by the cost per ride:
[tex]\[ \frac{36.00}{4.50} = 8 \][/tex]
So, Jay went on 8 rides.
The function to find the number of rides x is:
[tex]\[f(x) = 10.50 + 4.50x\][/tex]
Setting this equal to the total expenditure ($46.50), the function to find x is:
[tex]\[10.50 + 4.50x = 46.50\][/tex]
You buy a pair of jeans at a department store.
What is the percent of sales tax to the nearest tenth of a percent?
The price of the jeans includes a 60% markup. After the discount, what is the percent of markup to the nearest percent?
The price of the jeans before the discount is $24.99. The sales tax rate is 6.5%. The percent of markup after the discount is 27.7%.
The price of the jeans before the discount can be found by dividing the total cost by the markup percentage plus 100% and then multiplying by 100%.
So, the price of the jeans before the discount is (39.99 / 160) * 100 = 24.994375.
Next, to find the sales tax, multiply the subtotal by the sales tax rate.
The sales tax rate can be found by dividing the sales tax amount by the subtotal and then multiplying by 100%.
So, the sales tax rate is (1.95 / 29.99) * 100 = 6.502167.
To find the percent of markup after the discount, divide the difference between the total cost and the price before the discount by the price before the discount and then multiply by 100%.
So, the percent of markup after the discount is ((31.94 - 24.994375) / 24.994375) * 100 = 27.67322.
The probable question may be:
You buy a pair of jeans at a department store.
What is the percent of sales tax to the nearest tenth of a percent?
The price of the jeans includes a 60% markup. After the discount, what is the percent of markup to the nearest percent?
Department store
Jeans =39.99
Discount =-10.00
Subtotal =29.99
Sales tax=1.95
Total = 31.94
Evaluate the expression. [6(22 + 4)2 − 2(19 + 3)2]0
Answer:
the anwser is 1 so B)Step-by-step explanation:i just gottt it right on usa test prep
How Much Water Can Be Held By A Cylindrical Tank With A Radius Of 12 Feet And A Height Of 30 Feet
Where e is the region that lies inside the cylinder x2 + y2 = 16 and between the planes z = −4 and z = 1?
Final answer:
The region e refers to the inside of a cylinder defined by x² + y² = 16 and between the planes z = -4 and z = 1. It represents a three-dimensional space bounded both radially, by the cylinder, and vertically, by the planes.
Explanation:
The region described in the question is a cylindrical volume in three-dimensional space. To visualize this region, we remember that the cylinder is defined by the equation x2 + y2 = 16, which is the set of points in the xy-plane that are at a distance of 4 from the origin (since the radius is √16 = 4). This cylinder extends indefinitely in the positive and negative z-directions.
The planes z = -4 and z = 1 act as boundaries in the z-direction, trimming the cylinder down so that we're only considering the portion of the cylinder between these two planes. Thus the region e of interest is the set of points inside the cylinder that lie at a height between z = -4 and z = 1.
This type of region is common in problems involving volume calculations, especially when using integral calculus to determine the volume of the shape or when analyzing physical phenomena like fluid flow or electric fields within prescribed bounds.
Given the following triangle, if c = 17 and a = 15, find the measure of A. 28° 41° 62°
A biker traveled 20 miles in 4 hours. A unit rate to describe this would be 5 miles per hour. What is another unit rate in this situation?
92 divided by 4 use partial and quotients to divide
A shirt company has 3 designs that can be made with short or long sleeves. there are 6 color patterns available. how many different types of shirts are available from this company?
Answer: 36 Types
Step-by-step explanation:
3 designs and 6 color options so that would be
3 x 6 = 18
they also have the option of either long or short sleeve so that would be
18 x 2 = 36
2.1, -2.1, 2 and 2 1/11, -2 from least to greatest show work
Q: Write the slope intercept form of the equation of the line through the given point with the given slope.
Both problems; provide an explanation, please! Thank you!
A science fair poster is a rectangle
3
feet long and
2
feet wide. What is the area of the poster in square inches?
List all the factor pairs in the table factors of 25
solve the system by graphing or using a table 3x+y=5 x-y=7
In the last two years, Mari grew 2 1/4 inches, Kim grew 2.4 inches, and Kate grew 2 1/8 inches. Write the amounts they grew in order from least to greatest
Answer:
[tex]\text{Growth in Kate}<\text{Growth in Mari}<\text{Growth in Kim}[/tex]
Step-by-step explanation:
We are given the following information in the question:
Growth in Mari =
[tex]2\displaystyle\frac{1}{4}\text{ inches} = \frac{2\times 4 + 1}{4} = \frac{9}{4} = 2.25\text{ inches}[/tex]
Growth in Kim =
2.4 inches
Growth in Kate =
[tex]2\displaystyle\frac{1}{8}\text{ inches}= \frac{2\times 8 + 1}{8} = \frac{17}{8} = 2.125\text{ inches}[/tex]
Growth in order from least to greatest:
[tex]2.125<2.25<2.4\\\text{Growth in Kate}<\text{Growth in Mari}<\text{Growth in Kim}[/tex]
a person leaves their house to go to the store. it takes 15 minutes at 12 mph to get to the store. They return home at 31 mph. What is the average rate of the speed for the entire trip?